This paper was presented in ICDCN 2014.
Abstract: We propose two algorithm for solving self-stabilizing dining with Crash Locality 1 in asynchronous shared-memory systems with safe registers. Since this problem cannot be solved in pure asynchrony, we augment the shared-memory system with failure detectors. Specifically, we introduce the anonymous eventually perfect failure detector ?<>P (a variant of the anonymous perfect failure detector introduced by Guerraoui et al.), and show that this failure detector is sufficient to solve the problem at hand.
The preprint is available for download here.